The Global Positioning System (GPS) is a network of 24 satellites that is maintained by the United States Department of Defense and is used to determine the location of an antenna that passively receives signals from a number of these satellites. The GPS satellites are distributed among six orbits (four satellites per orbit) inclined at about 55.degree. from the equator, with consecutive satellite orbits being separated by about 60.degree. longitude across the equator. The four satellites in each orbit have roughly 12-hour orbits, and the number of satellites visible at any location on the Earth varies with time.
A range measurement is obtained from each satellite along with the location of the satellite at the time of measurement. The range measurement, referred to as pseudorange, is obtained by measuring the propagation time of the signal from the satellite to the user antenna. The pseudorange measurement has an additive component that is proportional to the relative frequency offset between the receiver oscillator and the satellite oscillator.
At least four GPS satellite pseudoranges are needed to solve for the antenna location because four unknowns are present: the (x,y,z) location coordinates of the receiver antenna in an Earth-centered, Earth-fixed (ECEF) coordinate frame, and the clock bias of the receiver oscillator relative to the GPS time frame. This is known as a three-dimensional location fix, because all three components of the antenna location are determined. The latitude, longitude and altitude of the antenna are easily computed from the (x,y,z) location coordinates with a well known coordinate transformation.
Altitude is generally understood to represent the height above sea level. The mean-sea-level (MSL) altitude of the antenna is found by converting the computed x,y,z position in ECEF coordinates into the height above a reference ellipsoid defined with the WGS-84 (World Geodetic Survey of 1984) model. This model takes into account the ellipticity of the Earth. A second model is used to obtain a correction between the ellipsoid model and mean-sea-level at the latitude and longitude computed from the ECEF coordinates (x,y,z). The MSL altitude is the difference between the MSL height and the local height of the reference ellipsoid.
Two factors affect the accuracy of the location fix. First, the pseudorange measurement from each satellite contains additive errors from a number of sources, such as errors in the satellite position, propagation-induced signal delays, errors from multipath signals, noise in the receiver, and intentionally induced errors from Selective Availability (SA). Second, the relative geometry of the satellites used for the solution controls how the measurement errors are incorporated into the location solution. A unit of measure of suitability of the satellite geometry is the dimensionless position dilution of precision (PDOP) parameter. The PDOP value helps determine how zero mean, unit variance errors, which are independent for each satellite, are scaled into errors in the location solution.
The PDOP parameter is well known in the practice of navigation and is calculated from a matrix of direction cosines, defined by projections of a unit vector extending from the receiver antenna to each satellite, onto selected coordinate axes. The PDOP value associated with a location fix computed using four pseudoranges is inversely proportional to the volume of the tetrahedron formed by first connecting these four unit vectors at the antenna location, and then connecting the other ends of the unit vectors into four planes, each of which is formed at ends of three of these unit vectors. The largest volume, and thus the smallest and best PDOP value, occurs when one satellite is directly overhead and the other three satellites are located near the horizon and spaced apart longitudinally 120.degree. from each other. The smallest volume, and thus the largest and worst PDOP value, occurs when the ends of the unit vectors all lie in the same plane. In this case, the volume is zero and the PDOP is infinite.
The PDOP parameter can be decomposed into horizontal and vertical dilution of precision components, HDOP and VDOP. Because the satellites are generally always above the horizon of the antenna, the VDOP parameter is generally at least twice as large as the HDOP parameter. A large portion of the measurement error is translated into the vertical direction error. For this reason, the vertical position accuracy tends to degrade faster than the horizontal accuracy when the PDOP value becomes large.
An estimate of the accuracy of the location fix is obtained by multiplying the PDOP value by an estimate of the pseudorange error standard deviation, expressed in length units. When SA is present, this error can be as large as 5-50 meters. With SA absent, a typical error is generally 5-15 meters. A good PDOP value is in the range 2-6. Thus, for this range of pseudorange errors, the accuracy of the position solution can vary from 10-90 meters without SA, and from 10-300 meters with SA. The DoD claims the inaccuracy of the horizontal position to be no more than 100 meters 95 percent of the time. This corresponds to a two-sigma horizontal position error with a range error standard deviation of 33 meters and an HDOP value of 1.5.
As the PDOP value becomes larger (say, PDOP&gt;6), the location accuracy begins to degrade significantly. In this case, a good three-dimensional location fix may be unavailable. Most GPS receivers have a maximum value of PDOP at which a three-dimensional location fix is performed; for larger PDOP values, the receiver may begin to compute a two-dimensional location fix instead. It is assumed that a satellite range measurement is available that is exactly in the vertical direction, which is equivalent to having a satellite at the center of the Earth. The range measurement is effectively the distance from the center of the Earth to the user antenna. This measurement is called an altitude fix because the altitude computed from the resulting (x,y,z) location fix is mathematically constrained to be the altitude used when the measurement is made. In other words, the measurement specifies what the altitude coordinate of the location solution will be.
A location solution computed with this type of measurement can be thought of as a three-dimensional location fix that is constrained to have a fixed component in the vertical direction. Thus, the location fix has only two degrees of freedom and is referred to as a two-dimensional location fix. As a result of this measurement, the VDOP value of the resulting location solution implicitly has a value of unity, because any altitude error in the measurement will be mapped into the altitude error of the location solution with a scale factor of 1. For most satellite geometries, use of an accurate altitude measurement will lower the overall PDOP value significantly, because of use of VDOP=1. Thus, two-dimensional navigation is possible with only three satellites, if the resulting HDOP value is less than a user-supplied limit.
The altitude measurement can also be included with the system of equations with more than three satellite measurements. In this case, the location solution is overdetermined; that is, more equations than unknowns are present. The resulting altitude solution will be a compromise between the altitude measurement and the altitude solution that would be available from the satellite-only vertical location solution. As a result, the altitude measurement must be weighted more heavily, in order to force the computed altitude to be close to the altitude supplied in the altitude measurement. Overdetermined solutions are a generalization of the solutions discussed here, where the number of measurements is assumed to be equal to the number of unknowns. In either case, the altitude measurement can be used to control the altitude of the computed ECEF location coordinates (x,y,z).
In summary, in at least two situations a need exists to stabilize the location solution. In a first situation, signals from fewer than four satellites are received, because other satellites are blocked by obstructions, or because only three satellites are available above the horizon. In a second situation, a good PDOP value from a four-satellite, three-dimensional location solution is not available. In these situations, a typical receiver adopts one of two modes. In a first mode, the receiver does not compute a location fix, because the user requested only three-dimensional fixes. In a second mode, the receiver goes into an altitude-hold mode, where the receiver assumes that the altitude is fixed, and uses this assumption to generate the fourth measurement needed to obtain a three-dimensional location solution. The altitude used is generally the last altitude computed from a three-dimensional GPS solution or from a reference altitude externally supplied to the receiver.
The receiver in altitude-hold mode cannot update the antenna altitude. If the receiver moves only in a horizontal plane, and if the assumed altitude is correct, the receiver will report the correct horizontal position, within the accuracy of the measurements and the associated PDOP value. However, if the user antenna changes altitude, or if the assumed altitude has a large error, large errors will be observed in both the horizontal and vertical location solutions. Thus, a user relying on this navigation system will not observe an altitude change when, in fact, the altitude is changing.
In this situation, the altitude sensor is of great value. When a three-dimensional location solution cannot be obtained with only GPS satellite signals, the altitude sensor can be used to generate an altitude measurement that can be added to the satellite measurements to generate a true three-dimensional location fix. Here, the altitude solution changes when the user antenna changes altitude and does not maintain a constant altitude as in altitude-hold mode.
Some workers have used elevation-measuring instruments in unconventional ways to increase the accuracy of location measurements. Evans et al disclose a digital altimeter computer using an atmospheric pressure transducer, in U.S. Pat. No. 4,292,671. The apparatus uses a predetermined local ground level pressure value and a nonlinear pressure-versus-altitude equation that takes different forms in two altitude ranges. Only the altitude coordinate A is determined here, and the formalism is apparently valid only for the range 1,000 ft.ltoreq.A.ltoreq.70,000 ft. above the Earth's surface. In particular, no account is taken of local variation of distance of the Earth's surface from the Earth's center.
A presentation system that magnifies and projects selected portions of a standard navigating chart is disclosed in U.S. Pat. No. 4,513,378, issued to Antkowiak. A vehicle carrying the system receives location-indicating signals from speed and direction sensors on the vehicle, from human input signals, and from radio waves transmitted from two or more Loran stations, and integrates these signals to estimate where the vehicle is presently located. The system then selects and projects a portion of the chart that includes this estimated present location and calculates a "course to steer" based on dead reckoning, manually entered information on nearby monuments, and other navigational aids.
U.S. Pat. No. 4,514,733, issued to Schmidtlein et al, discloses a navigational control system for aircraft that uses already-entered topographical data and terrain details, acquired by an earlier flight over the same territory and flight path as the present flight path. The reference material used to enter the topographical data may include stereo photos, topographic maps, etc. A radar transmitter and receiver, directed at the ground immediately below, is used to monitor the relative height of the aircraft along its flight path. No provision is made for receipt and analysis of altitude and horizontal location data that are presently gathered as the flight proceeds.
Chan et al, in U.S. Pat. No. 4,584,646, disclose a navigation system that compares terrain map correlation and dead reckoning location determination to determine horizontal, two-dimensional error estimates for the present location of an aircraft following a prescribed flight path. Previously measured terrain data, expressed in the frequency domain, are correlated with reference elevations stored in a map format and are used to improve the accuracy of a dead reckoning estimation of present location. An error is asserted to be determined for a barometric pressure altimeter used with the system, but the method for such determination is not discussed.
U.S. Pat. No. 4,829,304, issued to Baird, discloses a map-aided navigation system that uses TERCOM-SITAN control signals. An aircraft flies over terrain to be mapped and estimates aircraft location and altitude at a sequence of sampling points. These data are Kalman filtered, and the resulting filtered data are used to determine elevation and slope for this terrain. On a subsequent flight over this terrain, an aircraft uses altimeter sensing and the terrain map to determine the most likely flight path actually followed by the aircraft.
A navigation-by-correlation system for aircraft, using a relatively transparent atmospheric window (94 GHz) for measurements, is also disclosed by Lerche in U.S. Pat. No. 4,910,674. The aircraft is flown over a selected flight path, and the ground below is continually scanned in a direction transverse to the flight path direction. The system searches for an elevation that provides maximum correlation of the elevation reference data in a system computer with the location information received by the scanner. This approach requires that information on local elevation of the terrain flown over be already loaded into the system.
A vehicle navigation system that uses local topographical maps to correct an aircraft flight path is disclosed in U.S. Pat. No. 4,939,663, issued to Baird. During flight, local altitude measurements are made and used with a digital database containing local elevation (above a ground reference surface) of the Earth's surface. The location of the aircraft is sampled separately and is compared with the local elevation contour corresponding to the altimeter measurement; a location correction is determined that places the aircraft location over the elevation contour. Here, the local altitude coordinate of the aircraft is determined exclusively by the altimeter measurement, and the other two aircraft position coordinates are determined approximately by independent position sampling, which may use aircraft dead reckoning.
In U.S. Pat. No. 4,977,509, issued to Pitchford et al, a handheld, multi-purpose navigational instrument is disclosed that determines bearing, inclination, declination, temperature, barometric pressure, elapsed time and other variables. The apparatus uses an internal flux gate magnetometer for orientation information and uses a real time clock for time measurement, a foldable LCD display for navigation information, a keyboard for data entry and function choice, and a microprocessor for determining instrument two-dimensional location utilizing internal software and magnetometer measurements. Barometric pressure measurements, corrected for local temperature, are used to determine altitude or elevation.
Ando discloses a use of a vehicle-mounted GPS antenna and receiver for tracking GPS satellite signals without interruption when the vehicle passes through tunnels or urban canyons ("dead zones") and the GPS signals are temporarily lost, in U.S. Pat. No. 4,983,980. As soon as the vehicle emerges from the dead zone, the GPS receiver acquires a GPS signal from one satellite with the highest elevation angle, then begins to search for other GPS satellites, using known relative orbital positions for each GPS satellite. This approach is intended to reduce the time required for capture of GPS signals from a plurality of GPS satellites.
A map and text display system for aircraft navigation is disclosed by Factor et al in U.S. Pat. No. 5,057,835. The system stores terrain elevation information for regions adjacent to a flight path and compares the presently measured aircraft altitude with the maximum terrain elevation for the local region over which the aircraft is positioned, to determine if the aircraft altitude is above a safety threshold for that region. Aircraft latitude, longitude and altitude are determined conventionally, and no second source of aircraft altitude information is used to vary or improve the altitude estimate.
In U.S. Pat. No. 5,142,480, Morrow discloses method and apparatus for determination of a safe glide path for an aircraft approaching a landing site. The system uses horizontal location information provided by two or more Loran radiowave sources and vertical location information provided by an altimeter. The system provides backup calculations of all three location coordinates by the Loran information, if the altimeter is not operative. However, if the altimeter is operative, no integration of the altimeter readings and the Loran-determined vertical coordinate readings is performed.
A guidable airborne instrument module is disclosed in U.S. Pat. No. 5,186,418, issued to Lauritsen. The module, when released, receives signals from a plurality of ground-based beacons and determines the altitude and horizontal location of the module, for purposes controlling a module rudder to cause the module to controllably descend to a chosen landing site. An on-board radio transmitter broadcasts the present location of the module as the module descends.
Gloor, in U.S. Pat. No. 5,191,792, discloses a handheld navigation instrument that uses a magnetometer and a pressure sensor to provide information on the present heading and the present altitude, respectively, of a user. A microprocessor contained therein switches between a direction computation mode with LCD display and an altitude computation mode with LCD display.
In U.S. Pat. No. 5,202,829, Geier discloses a shipboard location determination system in which GPS-determined pseudorange values are passed through a Kalman filter. The Kalman-filtered pseudorange values PR are monitored to determine the quality of each such PR value in a weighted least squares location solution process. The location solutions can be visually displayed as error ellipses.
An on-board system for determination of the location of an airborne vessel, such as an aircraft, is disclosed in U.S. Pat. No. 5,208,757, issued to Appriou et al. The spatial coordinates of discrete landmarks on the terrain below are entered into a computer memory. As the vessel flies over a landmark, the known location of this landmark is used to correct the location given by another navigation means that uses images of small portions of the terrain below for location determination. Kalman filtering is applied to the location of the vessel relative to the terrain.
Masumoto discloses a GPS location determination system, supplemented by an altimeter, in U.S. Pat. No. 5,210,540. When three-dimensional GPS-determined location coordinates are available, the system ignores the altimeter, irrespective of the quality of the GPS signals. When only two location coordinates (latitude and longitude) are available using the GPS signals, the system uses the altimeter to provide a third (relative altitude) coordinate. No blending or optimization of the GPS and altimeter readings is disclosed or suggested. The system also stores measured altitude values for major roads and compares these values with the altimeter readings by map matching of latitude and longitude coordinates.
An integrated aircraft guidance system, using GPS, an inertial navigation system (INS) and a microwave landing system (MLS), is disclosed by McElreath in U.S. Pat. No. 5,216,611. The aircraft uses a Kalman filter to integrate GPS and INS navigation data for most of a point-to-point flight, until the aircraft comes within a few miles of the destination airport, where valid MLS data become available. The Kalman filter is then calibrated by the MLS data to permit precision landing using only the combined GPS/INS system, if MLS signals are lost during the landing. The locations determined by GPS/INS alone and by MLS alone are weighted to produce a composite location estimate, using only the distance d of the aircraft from the destination to determine the relative weights. The GPS/INS weight varies from 0.0 at d.ltoreq.5 nautical miles to 1.0 at d.gtoreq.10 nautical miles. No specific information is given on integration of the GPS and INS data.
U.S. Pat. No. 5,225,842, issued to Brown et al, discloses a vehicle tracking system that uses a GPS translator (not a full GPS receiver/processor) to sense certain GPS satellite signals at the vehicle. This GPS signal information is transmitted, unprocessed, to a remote GPS master station where this information is analyzed and the vehicle location and velocity are determined by post-processing. The master station can also employ satellite altitude maps and other aids, such as estimates of atmospheric time delays and clock offsets, to determine the changing locations of GPS satellites whose signals are received by the GPS translator on the vehicle.
A dead reckoning location detector and a GPS location determination system are combined for vehicle navigation in U.S. Pat. No. 5,257,198, issued to Hirata. GPS data are used preferentially to determine vehicle location, if GPS signals from at least three satellites are available. If these signals are not available, or if the GPS-determined distance the vehicle has traveled exceeds a predetermined threshold, dead reckoning is used exclusively to estimate the present vehicle location.
Hirata discloses a navigation system using a GPS location determination system, supplemented with altimeter information, in U.S. Pat. No. 5,265,025. If signals from four or more GPS satellites are available, three-dimensional coordinates for the user's present location are determined using standard GPS techniques. If signals from three or fewer GPS satellites are available, altimeter data are used to determine a vertical location coordinate, and the GPS signals are then used to determine two horizontal coordinates for the user's present location. This method takes no account of the relative quality of the vertical coordinate data produced by the altimeter and by the GPS.
In U.S. Pat. No. 5,345,241, Huddle discloses a method for correction of inertial navigation information, when an aircraft flies over water. An on-board barometric altimeter and radar altimeter measure the aircraft vertical distance above the surface of an ellipsoidal model of the Earth and above the water surface, respectively. An on-board computer determines the differences of these two distances for a plurality of points along the aircraft path. These differences are compared with reference to a model of undulation of the true surface with respect to the ellipsoidal surface to determine deviations of the actual aircraft path from an ideal path.
An altimeter-assisted re-entry vehicle (REV) inertial navigation system is disclosed in U.S. Pat. No. 5,355,316, issued to Knobbe. Altimeter readings are taken and combined with the inertial system determination on the altitude in a Kalman filter arrangement that provides a correction to the inertial system altitude fix.
What is needed is an approach that supplements location coordinates determined by a GPS with measurements of one or more location coordinates by another instrument, such as an altitude sensor, to improve the accuracy of the location coordinates and/or the availability of two-dimensional and three-dimensional location fixes. Preferably, this approach should allow an estimate of the reduction in inaccuracy that this combination produces, based upon estimatable inaccuracies for the individual approaches without such combination.